TSTP Solution File: NUM020^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM020^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:47:30 EDT 2024
% Result : Theorem 0.22s 0.52s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 25 unt; 6 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 129 ( 5 ~; 0 |; 0 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-4 aty)
% Number of variables : 50 ( 10 ^ 38 !; 2 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
two: ( $i > $i ) > $i > $i ).
thf(decl_25,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_28,type,
six: ( $i > $i ) > $i > $i ).
thf(decl_35,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_36,type,
esk1_2: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_37,type,
esk2_1: ( ( $i > $i ) > $i > $i ) > $i ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three )
= six ),
file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',thm) ).
thf(six_ax,axiom,
( six
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',six_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',three_ax) ).
thf(mult_ax,axiom,
( mult
= ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',mult_ax) ).
thf(two_ax,axiom,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',two_ax) ).
thf(c_0_5,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three )
= six ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_6,plain,
! [X18: $i > $i,X19: $i] :
( ( six @ X18 @ X19 )
= ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ X19 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).
thf(c_0_7,plain,
! [X12: $i > $i,X13: $i] :
( ( three @ X12 @ X13 )
= ( X12 @ ( X12 @ ( X12 @ X13 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_8,negated_conjecture,
! [X72: ( $i > $i ) > $i > $i] :
( ( mult @ X72 @ three )
!= six ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_9,plain,
! [X35: ( $i > $i ) > $i > $i,X36: ( $i > $i ) > $i > $i,X37: $i > $i,X38: $i] :
( ( mult @ X35 @ X36 @ X37 @ X38 )
= ( X35 @ ( X36 @ X37 ) @ X38 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_10,plain,
! [X51: $i > $i,X52: $i] :
( ( six @ X51 @ X52 )
= ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ X52 ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
! [X45: $i > $i,X46: $i] :
( ( three @ X45 @ X46 )
= ( X45 @ ( X45 @ ( X45 @ X46 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X10: $i > $i,X11: $i] :
( ( two @ X10 @ X11 )
= ( X10 @ ( X10 @ X11 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_13,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three )
!= six ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
! [X68: ( $i > $i ) > $i > $i,X69: ( $i > $i ) > $i > $i,X70: $i > $i,X71: $i] :
( ( mult @ X68 @ X69 @ X70 @ X71 )
= ( X68 @ ( X69 @ X70 ) @ X71 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X43: $i > $i,X44: $i] :
( ( two @ X43 @ X44 )
= ( X43 @ ( X43 @ X44 ) ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_18,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) )
!= ( six @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(neg_ext,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( mult @ X3 @ X4 @ X1 @ X2 )
= ( X3 @ ( X4 @ X1 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ ( three @ X1 @ X2 ) )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
thf(c_0_21,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( three @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) )
!= ( six @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( three @ X1 ) @ X2 )
= ( six @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_22,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM020^1 : TPTP v8.1.2. Released v3.6.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n007.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 09:05:50 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.22/0.50 Running higher-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p
% 0.22/0.52 # Version: 3.1.0-ho
% 0.22/0.52 # Preprocessing class: HSSSSMSSMSSNHHN.
% 0.22/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.52 # Starting pre_casc_2 with 1500s (5) cores
% 0.22/0.52 # Starting sh2 with 300s (1) cores
% 0.22/0.52 # Starting sh3 with 300s (1) cores
% 0.22/0.52 # Starting new_ho_10 with 300s (1) cores
% 0.22/0.52 # pre_casc_2 with pid 25218 completed with status 0
% 0.22/0.52 # Result found by pre_casc_2
% 0.22/0.52 # Preprocessing class: HSSSSMSSMSSNHHN.
% 0.22/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.52 # Starting pre_casc_2 with 1500s (5) cores
% 0.22/0.52 # No SInE strategy applied
% 0.22/0.52 # Search class: HUUPM-FFSF32-DHHSFMNN
% 0.22/0.52 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.52 # Starting pre_casc_2 with 901s (1) cores
% 0.22/0.52 # Starting sh2 with 151s (1) cores
% 0.22/0.52 # Starting sh3 with 151s (1) cores
% 0.22/0.52 # Starting sh9 with 151s (1) cores
% 0.22/0.52 # Starting new_ho_10 with 146s (1) cores
% 0.22/0.52 # new_ho_10 with pid 25232 completed with status 0
% 0.22/0.52 # Result found by new_ho_10
% 0.22/0.52 # Preprocessing class: HSSSSMSSMSSNHHN.
% 0.22/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.52 # Starting pre_casc_2 with 1500s (5) cores
% 0.22/0.52 # No SInE strategy applied
% 0.22/0.52 # Search class: HUUPM-FFSF32-DHHSFMNN
% 0.22/0.52 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.52 # Starting pre_casc_2 with 901s (1) cores
% 0.22/0.52 # Starting sh2 with 151s (1) cores
% 0.22/0.52 # Starting sh3 with 151s (1) cores
% 0.22/0.52 # Starting sh9 with 151s (1) cores
% 0.22/0.52 # Starting new_ho_10 with 146s (1) cores
% 0.22/0.52 # Preprocessing time : 0.001 s
% 0.22/0.52 # Presaturation interreduction done
% 0.22/0.52
% 0.22/0.52 # Proof found!
% 0.22/0.52 # SZS status Theorem
% 0.22/0.52 # SZS output start CNFRefutation
% See solution above
% 0.22/0.52 # Parsed axioms : 29
% 0.22/0.52 # Removed by relevancy pruning/SinE : 0
% 0.22/0.52 # Initial clauses : 29
% 0.22/0.52 # Removed in clause preprocessing : 14
% 0.22/0.52 # Initial clauses in saturation : 15
% 0.22/0.52 # Processed clauses : 52
% 0.22/0.52 # ...of these trivial : 3
% 0.22/0.52 # ...subsumed : 0
% 0.22/0.52 # ...remaining for further processing : 49
% 0.22/0.52 # Other redundant clauses eliminated : 0
% 0.22/0.52 # Clauses deleted for lack of memory : 0
% 0.22/0.52 # Backward-subsumed : 0
% 0.22/0.52 # Backward-rewritten : 3
% 0.22/0.52 # Generated clauses : 441
% 0.22/0.52 # ...of the previous two non-redundant : 435
% 0.22/0.52 # ...aggressively subsumed : 0
% 0.22/0.52 # Contextual simplify-reflections : 0
% 0.22/0.52 # Paramodulations : 431
% 0.22/0.52 # Factorizations : 0
% 0.22/0.52 # NegExts : 5
% 0.22/0.52 # Equation resolutions : 0
% 0.22/0.52 # Disequality decompositions : 0
% 0.22/0.52 # Total rewrite steps : 193
% 0.22/0.52 # ...of those cached : 146
% 0.22/0.52 # Propositional unsat checks : 0
% 0.22/0.52 # Propositional check models : 0
% 0.22/0.52 # Propositional check unsatisfiable : 0
% 0.22/0.52 # Propositional clauses : 0
% 0.22/0.52 # Propositional clauses after purity: 0
% 0.22/0.52 # Propositional unsat core size : 0
% 0.22/0.52 # Propositional preprocessing time : 0.000
% 0.22/0.52 # Propositional encoding time : 0.000
% 0.22/0.52 # Propositional solver time : 0.000
% 0.22/0.52 # Success case prop preproc time : 0.000
% 0.22/0.52 # Success case prop encoding time : 0.000
% 0.22/0.52 # Success case prop solver time : 0.000
% 0.22/0.52 # Current number of processed clauses : 31
% 0.22/0.52 # Positive orientable unit clauses : 11
% 0.22/0.52 # Positive unorientable unit clauses: 9
% 0.22/0.52 # Negative unit clauses : 11
% 0.22/0.52 # Non-unit-clauses : 0
% 0.22/0.52 # Current number of unprocessed clauses: 396
% 0.22/0.52 # ...number of literals in the above : 396
% 0.22/0.52 # Current number of archived formulas : 0
% 0.22/0.52 # Current number of archived clauses : 18
% 0.22/0.52 # Clause-clause subsumption calls (NU) : 0
% 0.22/0.52 # Rec. Clause-clause subsumption calls : 0
% 0.22/0.52 # Non-unit clause-clause subsumptions : 0
% 0.22/0.52 # Unit Clause-clause subsumption calls : 64
% 0.22/0.52 # Rewrite failures with RHS unbound : 0
% 0.22/0.52 # BW rewrite match attempts : 512
% 0.22/0.52 # BW rewrite match successes : 12
% 0.22/0.52 # Condensation attempts : 52
% 0.22/0.52 # Condensation successes : 0
% 0.22/0.52 # Termbank termtop insertions : 7770
% 0.22/0.52 # Search garbage collected termcells : 87
% 0.22/0.52
% 0.22/0.52 # -------------------------------------------------
% 0.22/0.52 # User time : 0.012 s
% 0.22/0.52 # System time : 0.004 s
% 0.22/0.52 # Total time : 0.016 s
% 0.22/0.52 # Maximum resident set size: 1832 pages
% 0.22/0.52
% 0.22/0.52 # -------------------------------------------------
% 0.22/0.52 # User time : 0.064 s
% 0.22/0.52 # System time : 0.011 s
% 0.22/0.52 # Total time : 0.075 s
% 0.22/0.52 # Maximum resident set size: 1744 pages
% 0.22/0.52 % E---3.1 exiting
% 0.22/0.53 % E exiting
%------------------------------------------------------------------------------